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On the Robust Capability of Feedback Scheduling in ORB Middleware Bing Du David.C. Levy School of Electrical and Information Engineering University of Sydney The University of Sydney

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Outline of presentation Introduction. H∞control scheduling Architecture. H∞ robust controller and H∞-NMPC controller. Overview of hORB Architecture Conclusion

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Introduction Traditional scheduling are no longer promise the function and performance requirements of DRE systems. The common ORB middleware scheduling approaches can’t provide real-time performance guarantees because they depend on accurate task execution times.

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Introduction Many recent scheduling research approaches have applied feedback control theory, but little theoretical analysis has been provided about effects of the plant uncertainty and nonlinearity on the desired system performance. H∞-nonlinear model predictive control scheduling (H∞-NMPC) is provided an excellent theoretical framework for dealing with nonlinear stability and robustness issues by H∞ theory.

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H∞ control scheduling Architecture Task model U = e / d – r. Requested CPU utilization U,release time r, execution time e, deadline d The performance can be interpreted as a quality-of- service (QoS) measure. The system will control the rate of deadline misses by regulating the QoS of the task.

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H∞ control scheduling Architecture

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H∞ robust controller The physical process is a nonlinear model and can be treated in continuous time, with continuous signals, while the controller is a discrete time algorithm Tustin transform to transform continuous systems into discrete systems and back again: S =2(z-1) / T(z+1)

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Generalized nonlinear discrete-time H∞ system P is an LTI system; f(q) is a static nonlinearity; and Δ is a block structured, norm bounded perturbation

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H∞ robust controller Transfer function from w to e e = F ℓ [ F u ( P ( s ), Δ ), K ( s )] w = G ( s ) w satisfies a norm objective The problem is to design K(s) such that for all Δ BΔ, K (s) stabilizes Fu(P(s), Δ), and || F u ( F ℓ ( P (s), K (s) ), Δ || ≤ 1. This is equivalent to K (s) satisfying μ [ F ℓ ( P ( s ) ; K ( s ) )]<1

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H∞-NMPC controller Based on the derivation of a stationary Hamilton-Jacobi-Isaacs equation, which is the nonlinear analogous of the FHARE (fake H∞ algebraic Riccati equation), it is shown that the H∞ NMPC control law is the solution of an associated infinite horizon H∞ control problem,

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H∞-NMPC controller a class of systems described by the following nonlinear set of differential equations: (t) = f ((t), u (t)), (0) = where (t) and u (t) denotes the vector of states and inputs, respectively.

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H∞-NMPC controller The finite horizon open-loop problem described above is mathematically formulated as follows: find min J ((t), ū (∙); Tc, Tp) ū (∙) with J ( x (t), ū (∙); Tc, Tp) = where Tc and Tp denotes control horizon and prediction horizon, and ū (∙) denotes the internal input.

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Generalized and weighted performance block diagram

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DK iteration The current approach to design a controller is known as DK iteration. Suppose that K(s) stabilizes P (s) and ||F(P (s); K(s))|| ≤ 1 This is an upper bound for the μ problem, implying that, μ[F(P (s); K(s))] ≤ 1 The μsynthesis problem can be replaced with the following approximation inf || DF(P (s); K(s))D‾¹ || DЄ Đ K(s) stabilizing

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Two tank system model to emulate a scheduling system Design a controller that regulates the levels in tank2, h2. The task actuator controls the flow into the system. The tasks that adds the height of liquid tank 2 not higher than 100 cm can be admitted. QoS actuator can adjust the tank 2 liquid higher or lower so that the level keeps at 100 cm. The deadlines of accepted tasks can be achieved by EDF if the height of liquid tank 2 is below 100 cm.

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Two tank system model of scheduling system

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Tracking simulation perturbed system with +10% change. The inputs are constrained to remain within 25-75%

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Overview of hORB Architecture This framework is based on AMIDST [21] and deploys the advanced control theory mechanisms to provide deadline miss ratio and utilization guarantees and to adapt execution environment to variation in the resource availability. The H∞-NMPC/connection threads on the server are connected with each client connection thread through a TCP connection called feedback lane. Each client receives the new QoS parameter for its remote method invocation requests from translator on the server through the feedback lane.

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hORB Architecture

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Conclusion Our mechanism give a systematically and theoretically platform to investigate how to deal with uncertainty and additive disturbance for real-time system and how to design a H∞ control scheduling. The experimental results show that proposed scheduler improves the robust stable performance for uncertain real-time systems even when system parameters and workload vary.

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